On Wed, 1 Nov 2017 19:57:59 +0000
(D.M. Procida) wrote:

I'm going to rewire an old, old 35mm projector, a Picturol Model Q -
one of these:
https://img0.etsystatic.com/054/0/7703457/il_570xN.744183042_m3td.jpg.

It was wired with a two-core flex, but since the body is metal I
wonder whether it would be better to rewire it with three, earthing
the metal body.

The flex connects directly to the terminals of the lamp socket; if the
live connection were to work loose I could imagine it making contact
with the body of the projector.

I have a vintage sewing machine that I was happily using with live
shorted to the metal body, until one day I happened to ground myself
against something and felt a tingle. As long as you don't use
something like that while soaking wet and holding onto a water pipe
you'll probably be fine. So my choice would be to keep it original,
but other people may be more sensitive to/about mains voltage.